Modeling fractured wells

ABSTRACT

Disclosed are methods, systems, and computer-readable medium to perform operations including: receiving, by a computing device, parameters of the fractured well, wherein the fractured well comprises a wellbore and one or more hydraulic fractures extending from the wellbore; generating, by the computing device and based on the parameters of the fractured well, an equivalent complex well that represents the fractured well; and executing, by the computing device and using the equivalent complex well, a simulation that simulates the performance of the fractured well.

TECHNICAL FIELD

The present disclosure relates to modeling fractured wells.

BACKGROUND

In the oil and gas industry, hydraulic fracturing is used to perform awell stimulation treatment that negates near-wellbore damage caused bydrilling operations or creates improved paths for fluid to flow fromformations to wells. A hydraulically fractured well (or “fracturedwell”) includes a wellbore (for example, a horizontal wellbore) andfractures that extend from the wellbore into the formation. Hydraulicfracturing is a complex engineering operation that requires knowledge inreservoir engineering, fluid flow in porous media, rock elasticity, andgeomechanics.

SUMMARY

Several factors are important for establishing successful hydraulicfracturing operations, including detailed design of hydraulic fractures,careful operation and execution, and accurate modeling of hydraulicfractures. There are existing simulators that model fractured wells forthe purposes of history matching and predicting well performance (forexample, hydrocarbon flow, formation pressure, and hydrocarbonproduction). Many of these simulators use grid refinement to explicitlyrepresent hydraulic fractures in simulation models. Grid refinement,also called a local grid refinement (LGR) process, refines coarse gridblocks into smaller cells.

However, existing simulators have many deficiencies. As an example,existing simulators are merely capable of assessing the performance of asingle fractured well. Such an assessment misses important informationrelated to areas surrounding the fractured well. Further, the type ofmodeling performed by existing simulators is considered anapproximation, at best, since many assumptions on which the simulatorsoperate are inaccurate. For example, existing simulators assume thathydraulic fractures are uniform in production and performance, whereasin reality, hydraulic fractures are not uniform. Additionally, existingsimulators do not capture the individual parameters of hydraulicfractures, such as fracture half length (X_(f)), fracture width (W_(f)),and fracture height (h_(f)). Furthermore, existing simulators are notcapable of generating simulation results not on the hydraulic fracturelevel. In sum, existing simulators provide inaccurate approximations andare not capable of generating individual performance profiles forhydraulic fractures.

This disclosure describes methods and systems for modeling fracturedwells, for example, on a full field scale. Aspects of the subject matterdescribed in this specification may be embodied in methods that includethe operations for simulating performance of a reservoir that includes afractured well. Disclosed are methods, systems, and computer-readablemedium to perform operations including: receiving, by a computingdevice, parameters of the fractured well, where the fractured wellincludes a wellbore and one or more hydraulic fractures extending fromthe wellbore; generating, by the computing device and based on theparameters of the fractured well, an equivalent complex well thatrepresents the fractured well; and executing, by the computing deviceand using the equivalent complex well, a simulation that simulates theperformance of the fractured well.

The previously-described implementation is implementable using acomputer-implemented method; a non-transitory, computer-readable mediumstoring computer-readable instructions to perform thecomputer-implemented method; and a computer system including a computermemory interoperably coupled with a hardware processor configured toperform the computer-implemented method or the instructions stored onthe non-transitory, computer-readable medium. These and otherembodiments may each optionally include one or more of the followingfeatures.

In some implementations, the equivalent complex well is a multilateralwell that includes a motherbore and one or more lateral wellbores, wherethe motherbore represents the wellbore of the fractured well, and whereeach lateral wellbore represents a respective hydraulic fracture.

In some implementations, the parameters of the fractured well include atleast one of: (i) a length of the wellbore, (ii) respective fracturehalf-lengths (X_(f)) of the one or more hydraulic fractures, (iii)respective fracture heights (h_(f)) of the one or more hydraulicfractures, (iv) respective fracture widths (W_(f)) of the one or morehydraulic fractures, or (v) a hydraulic fracture spacing intensity.

In some implementations, generating, by the computing device and basedon the parameters of the fractured well, the equivalent complex wellinvolves: modeling each hydraulic fracture by a respective rectangulartube, where dimensions of the respective rectangular tube is based ondimensions of the hydraulic fracture.

In some implementations, generating, by the computing device and basedon the parameters of the fractured well, the equivalent complex wellfurther involves: generating a motherbore of the equivalent complex wellto represent the wellbore of the fractured well.

In some implementations, generating, by the computing device and basedon the parameters of the fractured well, the equivalent complex wellfurther involves: converting the respective rectangular tube into arespective wellbore, where the respective wellbore has an equivalentwellbore diameter calculated based on the dimensions of the respectiverectangular tube, and where a length of the respective wellbore is equalto a height of the respective rectangular tube.

In some implementations, executing, by the computing device and usingthe equivalent complex well, the simulation involves: generating, usinga multi-segmentation approach, a model of the equivalent complex well,where the model includes one or more respective segments for at leastone of the wellbore or the one or more hydraulic fractures.

In some implementations, executing, by the computing device and usingthe equivalent complex well, the simulation further involves: generatinga computation matrix for the model of the equivalent complex well, wherethe wellbore computational matrix includes a system of linear algebraicequations that represent at least one of mass balance equations,momentum balance equations, or energy balance equations for the one ormore respective segments; and solving the computation matrix anddetermining that a solution to the computation matrix has converged toan acceptable tolerance.

In some implementations, the operations further involve generating,based on the simulation, at least one graph that represents individualproduction and performance profiles for the one or more hydraulicfractures; and causing, by the computing device, a display device todisplay the at least one graph.

In some implementations, the operations further involve: determining,based on the simulation, a hydraulic fracture design of a well to bedrilled; and controlling, by the computing device, at least one drillingdevice to drill the well according to the hydraulic fracture design.

In some implementations, the operations further involve coupling asolution of the simulation to a reservoir simulation, where the couplingis explicit, sequential, or implicit.

The subject matter described in this specification can be implemented inparticular implementations so as to realize one or more of the followingadvantages. The disclosed techniques can individually model eachhydraulic fracture of a fractured well. More specifically, the disclosedtechniques facilitate a fracture level representation and modificationfor each hydraulic fracture. As such, the disclosed techniques can modelnon-uniform fractures that have different properties. The disclosedtechniques also enable wellbore level modifications to match individualfracture performance without the need to alter geological reservoirproperties. By matching the fracture contribution to historicalperformance, a more accurate prediction of future performance can beobtained, for example, for field development planning activities. Thisfacilitates practical planning for future wells to be drilled withhydraulic fracture designs that ensure effective stimulation jobs,thereby improving well productivity and recovery. Further, the disclosedtechniques can be performed on a large scale field level for reservoirsthat include hundreds to thousands of wells of different types. Thisachieves “big picture” modeling for reservoirs.

The details of one or more implementations of the subject matter of thisspecification are set forth in the Detailed Description, theaccompanying drawings, and the claims. Other features, aspects, andadvantages of the subject matter will become apparent from the DetailedDescription, the claims, and the accompanying drawings.

DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an example multi-segment model for a complex well,according to some implementations of the present disclosure.

FIG. 2 illustrates a workflow for simulating a fractured well, accordingto some implementations of the present disclosure.

FIG. 3 illustrates a side view of a fractured well, according to someimplementations of the present disclosure.

FIG. 4A and FIG. 4B illustrate hydraulic fractures modeled asrectangular tubes, according to some implementations of the presentdisclosure.

FIG. 5 illustrates an equivalent complex well that represents afractured well, according to some implementations of the presentdisclosure.

FIG. 6 illustrates a workflow for implicitly simulating a reservoir thatincludes a fractured well, according to some implementations of thepresent disclosure.

FIG. 7 illustrates a flowchart of an example method, according to someimplementations of the present disclosure

FIGS. 8, 9A, 9B, 9C, 9D, 9E, and 10 illustrate results of a firstsimulation that implements a disclosed workflow, according to someimplementations of the present disclosure.

FIGS. 11 and 12 illustrate results of a second simulation thatimplements a disclosed workflow, according to some implementations ofthe present disclosure.

FIG. 13 illustrates a block diagram illustrating an example computersystem used to provide computational functionalities associated withdescribed algorithms, methods, functions, processes, flows, andprocedures as described in the present disclosure, according to someimplementations of the present disclosure.

FIG. 14 illustrates a partial schematic perspective view of an examplerig system for drilling and producing a well, according to someimplementations of the present disclosure.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This disclosure describes techniques for modeling fractured wells. Insome embodiments, the techniques model a fractured well as a complexwell, perhaps by generating a complex well (referred to in thisdisclosure as an “equivalent complex well”) that represents thefractured well. Compared to existing modeling techniques, modeling thefractured well as a complex well achieves a more accurate representationof hydraulic fracture geometry. For example, modeling the fractured wellas such enables modeling the individual parameters of hydraulicfractures. In some embodiments, the equivalent complex well is amultilateral well. In these embodiments, a wellbore of the fracturedwell is represented by a motherbore of the multilateral well, andhydraulic fractures of the fractured well are represented by lateralwellbores of the multilateral well. The disclosed techniques then usecomplex well modeling to simulate performance of the equivalent complexwell, thereby simulating performance of the fractured well. Simulatingperformance of the fractured well provides information indicative ofhydrocarbon recovery, such as hydrocarbon flow and pressure under one ormore producing scenarios.

Generally, complex well modeling is used to model complex wells such ashorizontal, multilateral, maximum reservoir contact (MRC), and extendedreach drilling (ERD) wells. A multilateral well has two or more lateralwellbores (also referred to as laterals) that extend from a primarywellbore (also referred to as a motherbore). The laterals can behorizontal, vertical, or deviated from the primary wellbore. Complexwell modeling can model various aspects of complex wells, includingpressure losses, multiphase effects, and mechanical devices (forexample, internal control devices and interval control valves).

Complex well modeling uses a multi-segmentation approach or a generalnetwork graph approach. In the multi-segmentation approach, welltrajectories are divided into a plurality of segments. Then, transferequations (for example, mass balance equations, momentum balanceequations, and energy balance equations) are generated for each segment.During a simulation, the transfer equations are solved for each segment.On the other hand, in the general network graph approach, welltrajectories are divided into nodes and links. In this approach, linksrepresent well segments and mechanical devices, and nodes representsconnections between the links. During a simulation, mass balanceequations and momentum balance equations are solved for each link ornode, where molar rate is a link property and pressure is a nodeproperty. Additionally, well operating conditions, such as rates andpressures, are formulated as constraint equations that serve as boundaryconditions for solving the complex well model.

FIG. 1 illustrates an example multi-segment model 100 for a complexwell, according to some implementations. In this example, the complexwell is a multilateral well that includes a primary wellbore 102, amotherbore 106, and laterals 104, 108 that branch from the motherbore106. The section of the motherbore 106 that meets the primary wellbore102 is referred to as a heel, and the opposite end of the motherbore isreferred to as a toe. As shown in FIG. 1 , the multi-segment model 100includes one or more respective segments for each of the motherbore 106and the laterals 104, 108. The one or more respective segments arelabelled as segments 1-24. During a simulation, transfer equations aresolved for each segment.

FIG. 2 illustrates a workflow 200 for simulating a fractured well,according to some implementations. As described below, the workflow 200generates an equivalent complex well that represents the fractured well.In an example, the equivalent complex well is a multilateral well. Inthis example, a wellbore of the fractured well is represented by amotherbore of the multilateral well, and hydraulic fractures of thefractured well are represented by lateral wellbores of the multilateralwell. Once the equivalent complex well is generated, complex wellmodeling (for example, multi-segmentation) is used to simulateperformance of the fractured well by simulating performance of theequivalent complex well.

In some embodiments, the workflow 200 is performed by one or morecomputing systems, for example, the computer system 1300 of FIG. 13 , orby any suitable system, environment, software, hardware, or acombination of systems, environments, software, and hardware, asappropriate. In the following discussion of the workflow 200, referenceis also made to FIG. 3 , FIG. 4A, FIG. 4B, FIG. 5 , and FIG. 6 .Additionally, although the following discussion describes simulating asingle fractured well, the workflow 200 can consecutively orsimultaneously simulate a plurality of both non-fractured and fracturedwells (for example, on the order of tens or hundreds of wells).

At step 202, the workflow 200 involves receiving, perhaps from adatabase or user input, parameters of the fractured well. The parametersof the fractured well include wellbore parameters and hydraulic fractureparameters. The wellbore parameters include a length of the wellbore,and the hydraulic fracture parameters include a fracture half-length(X_(f)), a fracture height (h_(f)), a fracture width (W_(f)) of eachhydraulic fracture. In some examples, step 202 also involves receiving ahydraulic fracture spacing intensity. Hydraulic fracture spacingintensity spacing intensity refers to a minimum distance to maintainbetween adjacent fractures when designing a hydraulic fractures job.

FIG. 3 illustrates a side view 300 of a fractured well, according tosome implementations. The fractured well includes a wellbore andhydraulic fractures that extend from the wellbore. In some examples, ahydraulic fracture includes two wings, each of which extend fromopposite sides of the wellbore. In FIG. 3 , the fractured well includesa horizontal wellbore 302 and a hydraulic fracture 304. The hydraulicfracture 304 includes wings 306 a, 306 b that extend from the horizontalwellbore 302 into the formation. As shown in FIG. 3 , a half-length(X_(f)) of the hydraulic fracture 304 is a distance from the horizontalwellbore 302 to a distal point of the hydraulic fracture 304. That is,the half-length is a length of one wing of the hydraulic fracture 304.

Returning to FIG. 2 , at step 204, the workflow 200 involves modelingthe hydraulic fractures as rectangular tubes. This step is performed inpreparation for generating an equivalent complex well that representsthe fractured well in the next step. In some examples, the hydraulicfractures are modeled as rectangular tubes that extend in orthogonaldirections from the wellbore. The dimensions of the rectangular tubesare based on the geometries of the hydraulic fractures. Morespecifically, a rectangular tube that represents a hydraulic fracturehas a length equal to two times the half-length of that hydraulicfracture (that is, length=2*X_(f)), a width equal to the fracture widthof that hydraulic fracture (that is, width=W_(f)), and a height equal tothe fracture height of that hydraulic fracture (that is, height=h_(f)).In some examples, a rectangular tube that represents a hydraulicfracture includes two sections, each of which represents one wing of thehydraulic fracture. In these examples, each rectangular section has aheight equal to h_(f), a width equal to W_(f), and a length equal toX_(f).

FIG. 4A and FIG. 4B illustrate hydraulic fractures modeled asrectangular tubes, according to some implementations. FIG. 4Aillustrates a top view 400 of a fractured well that includes ahorizontal wellbore 402 and hydraulic fractures. The hydraulic fracturesare represented as rectangular tubes 404 a, 404 b, 404 c, 404 d, and 404e that extend orthogonally from the horizontal wellbore 402. In thisexample, the hydraulic fractures have identical geometries, andtherefore, the rectangular tubes 404 a, 404 b, 404 c, 404 d, and 404 ehave identical dimensions. That is, each rectangular tube has a lengthequal to 2*X_(f) and a width equal to W_(f). FIG. 4B illustrates aperspective view 410 of a section 412 of a rectangular tube thatrepresents one wing of a hydraulic fracture. As shown in FIG. 4B, thesection 412 has a height equal to h_(f), a width equal to W_(f), and alength equal to X_(f).

Returning to FIG. 2 , at step 206, the workflow 200 involves generatingan equivalent complex well that represents the fractured well. In thisstep, the wellbore of the fractured well is modeled as a motherbore of amultilateral well. Further, the hydraulic fractures are modeled as openhole laterals that emanate from the motherbore. In order to model thehydraulic fractures as such, the rectangular tubes are converted intolateral wellbores. To convert a rectangular tube into a lateral, anequivalent wellbore diameter for the lateral is calculated. Theequivalent wellbore diameter is used to calculate a circular equivalentto a rectangular tube. In an example, the equivalent wellbore diameteris calculated using Equation (1), which is an equation for calculating ahydraulic diameter of a rectangular tube:

$\begin{matrix}{{{{Equivalent}{Diameter}(d)} = {4 \times \frac{Area}{Perimeter}}},.} & {{Equation}(1)}\end{matrix}$

As shown in Equation (1), the equivalent wellbore diameter of arectangular tube is based on an area and a perimeter of the tube. InEquation (2), the equivalent wellbore diameter of a rectangular tubethat represents a hydraulic fracture is calculated using a fracturehalf-length (X_(f)) and a fracture width (W_(f)) of the hydraulicfracture:

$\begin{matrix}{{d = {4 \times \frac{2X_{f} \times W_{f}}{2 \times \left( {{2 \times X_{f}} + W_{f}} \right)}}},.} & {{Equation}(2)}\end{matrix}$

Thus, each hydraulic fracture is represented using a lateral wellbore(that is, a circular wellbore) that has a diameter equal to thecalculated equivalent diameter for that hydraulic fracture, and a lengthequal to the fracture height (h_(f)) of that hydraulic fracture.

FIG. 5 illustrates an equivalent complex well 500 that represents afractured well, according to some implementations. In FIG. 5 , ahorizontal motherbore 502 represents the wellbore of the fractured well(for example, the horizontal wellbore 402). Further, vertical lateralwellbores 504 a, 504 b, 504 c, 504 d, and 504 e, which are orthogonal tothe horizontal motherbore 502, represent the hydraulic fractures of thefractured wellbore (for example, the hydraulic fractures 404 a, 404 b,404 c, 404 d, and 404 e). Each vertical lateral wellbore has arespective equivalent diameter that is calculated based on thedimensions of the corresponding hydraulic fracture. Further, eachvertical wellbore has a length equal to the respective fracture height(h_(f)) of the corresponding hydraulic fracture.

Returning to FIG. 2 , at step 208, the workflow 200 involves performinga simulation using the equivalent complex well. By performing asimulation using the equivalent complex well, the fractured well isbeing simulated. In this step, complex well modeling techniques, such asthe multi-segmentation approach or the general network approach, areused to model the equivalent complex well. For instance, themulti-segmentation approach can be used to segment the equivalentcomplex well into one or more segments. More specifically, each of themotherbore and the laterals can be segmented into one or more respectivesegments. Equivalently, the wellbore of the fractured well and thehydraulic fractures of the fractured well are being segmented into oneor more respective segments.

In some embodiments, an input simulation file that includes a detailedphysical representation of the fractured well is generated. In exampleswhere the multi-segmentation approach is used, the input simulation fileincludes a system of linear algebraic equations that represent at leastone of mass balance equations, momentum balance equations, or energybalance equations for the segments of the complex well. The inputsimulation files can be run by a grid simulator to compute theperformance of the fractured well (for example, hydrocarbon flow andhydrocarbon production) and to generate individual production andperformance profiles (for example, pressure and flow rate profiles) forthe hydraulic fractures of the fractured well. During the simulation,detailed computations of pressure and flow rate profiles are performedfor the segments of the complex well.

In some embodiments, the grid simulator simulates the equivalent complexwell as part of an overall reservoir simulation. In these embodiments,the grid simulator performs the reservoir simulation in two steps. Inthe first step, the equivalent complex well is simulated. In the secondstep, the solution of the complex well simulation is coupled to thereservoir simulation. In one example, the equivalent complex well issimulated by generating a Jacobian matrix that includes the system oflinear algebraic equations that is associated with the equivalentcomplex well. The grid simulator solves the Jacobian matrix, perhapsusing the Newton-Raphson method. The Newton-Raphson method iterativelysolves the Jacobian matrix until the solutions to the Jacobian matrixconverge; for example, satisfy a predetermined tolerance, perhaps of thespectral radius of the iteration. The predetermined tolerance for theconvergence is an absolute or relative tolerance on change of individualvariables (convergence on change) and/or a predefined tolerance forchange of residual (convergence on residual). Further, during eachNewton iteration, the Newton-Raphson method calculates and solves anupdated Jacobian matrix. Once the solutions converge, they are thencoupled with the reservoir simulation. The coupling can be explicit,sequential, or implicit.

In some embodiments, the solutions to the equivalent complex well areimplicitly coupled to the reservoir simulation. In these embodiments,the equivalent complex well is solved together as one system with thereservoir grid. The boundary condition of the equivalent complex well isupdated for each iteration. Further, both the reservoir grid and theequivalent complex well are solved in each Newton iteration.Specifically, the Jacobian matrix for the whole system, including thereservoir grid and the equivalent complex well, is built and the wholesystem is solved implicitly. If the solution converges, the gridsimulator proceeds to the next time step. Otherwise, the grid simulatorgoes back to the Newton iteration. FIG. 6 shows the workflow of theimplicit coupling to solve the whole system.

FIG. 6 illustrates a workflow 600 for implicitly simulating a reservoirthat includes a fractured well, according to some implementations. Theworkflow 100 involves performing the simulation for n time steps, asshown by block 602. During each time step, the Newton-Raphson method isiteratively performed over k Newton iterations, as shown by block 604.During a Newton iteration, the grid simulator solves a Jacobian matrixthat represents an equivalent complex well, as shown by block 606.Specifically, the grid simulator solves for A_(N) (the Jacobian matrixfor complex well network) using A_(N)X_(N)=b_(N), where X_(N) isvariables in a complex well network and b_(N) is a residual for thecomplex well network. The grid simulator then builds a Jacobian matrixfor the reservoir, as shown by block 608. Then, the grid simulatorsolves the Jacobian matrix for the reservoir, as shown by block 610. Thevariables of the equation in block 610 are defined as:

-   -   A_(G): Jacobian matrix for the grid    -   A_(GN): Jacobian matrix for grid to network    -   A_(NG): Jacobian matrix for network to grid    -   X_(G): Variables in grid system    -   b_(G): Residual for grid        As shown by block 612, the grid simulator updates the solutions        based on the solved Jacobian matrix for the reservoir. The grid        simulator then determines whether the updated solutions have        converged, as shown by block 614. If the solutions have        converged, the grid simulator proceeds to the next time step.        And if the solutions have not converged, the grid simulator        proceeds to the next Newton iteration for the current time step.

In some embodiments, the grid simulator generates individual productionand performance profiles for the hydraulic fractures of the fracturedwell. The simulation results include respective fracture productioninformation for each fracture. Additionally, the simulation resultsinclude detailed results for each fracture. The detailed results for afracture include the results corresponding to one or more segments thatrepresent the fracture. Example simulation results are illustrated inFIGS. 8-12 .

Returning to FIG. 2 , at step 210, the workflow 200 involves historymatching the simulated hydraulic fracture performance. In this step, oneor more factors are applied to the simulation results of the hydraulicfractures. Because the hydraulic fractures are modeled individually, theone or more factors can be applied to a subset of the modeled hydraulicfractures or all of the modeled hydraulic fractures. Further, values ofthe one or more factors can be identical or different for differentmodeled hydraulic fractures. In scenarios where more than one segment isused to model a hydraulic fracture, the one or more factors can beapplied individually to each segment. Thus, different values of the oneor more factors can be selected for each segment of the same modeledhydraulic fracture. The workflow 200 has the flexibility to choose andselect certain segments along the fracture length at which to apply skinfactors. This achieves high definition history matching for fracturedwells.

In some embodiments, the one or more factors include a productivityindex (PI) multiplier, a skin factor multiplier, and a hydraulicfracture roughness. PI is a measure of a well's potential to produce andcan be computed using Equation (3):

$\begin{matrix}{J = {\frac{Q}{\left( {P_{r} - P_{wf}} \right)}.}} & {{Equation}(3)}\end{matrix}$

In Equation (3), Q is a production flow rate in stock tank barrel/day(stb/d), P_(r) is a reservoir static pressure in pounds per square inch(psi), and P_(wf) is a well bottom hole flowing pressure in psi. The PImultiplier is a modification factor that has a value greater than zero.This factor is used to modify the simulation model flow rate and bottomhole pressure by increasing or decreasing it in order to match measuredproduction performance without changing reservoir properties, such asporosity, permeability, or saturation. In complex well modeling, arespective segment PI multiplier can be applied to one or more modeledsegments (for example, a fracture or a portion thereof).

Skin is a dimensionless estimation of flow stoppage or jam. The skinvalue can be positive which indicates wellbore damage or an obstruction(for example, due to excess heavy weight drilling fluid damage to theformation). A negative skin value, on the other hand, reflectsimprovement in the flow path and significant reduction to formationdamage. The skin factor is used to improved or reduce simulation modelflow rate in order to match a tested production flow rate of aparticular well. For hydraulic fractures, the skin factor is applied atone or more segments to mimic a measured performance profile.

Hydraulic fracture roughness refers to the changes or irregularities inthe surface texture of a hydraulic fracture. Hydraulic fractureroughness results in a pressure drop referred to as friction ΔP. Whenhistory matching hydraulic fracture performance, roughness values areused to improve pressure match with certain flow rates.

FIG. 7 illustrates a flowchart of an example method 700 for simulatingperformance of a fractured well, according to some implementations. Forclarity of presentation, the description that follows generallydescribes method 700 in the context of the other figures in thisdescription. For example, the method 700 can be performed by thecomputer system 1300 of FIG. 13 . However, it will be understood thatthe method 700 may be performed, for example, by any suitable system,environment, software, and hardware, or a combination of systems,environments, software, and hardware, as appropriate. In someimplementations, various steps of the method 500 can be run in parallel,in combination, in loops, or in any order.

At step 702, method 700 involves receiving, by a computing device,parameters of a fractured well, where the fractured well includes awellbore and one or more hydraulic fractures extending from thewellbore. In some examples, the parameters of the fractured well includeat least one of: (i) a length of the wellbore, (ii) respective fracturehalf-lengths (X_(f)) of the one or more hydraulic fractures, (iii)respective fracture heights (h_(f)) of the one or more hydraulicfractures, (iv) respective fracture widths (W_(f)) of the one or morehydraulic fractures, or (v) a hydraulic fracture spacing intensity. FIG.3 illustrates an example fractured well.

At step 704, method 700 involves generating, by the computing device andbased on the parameters of the fractured well, an equivalent complexwell that represents the fractured well. In some examples, theequivalent complex well is a multilateral well that includes amotherbore and one or more lateral wellbores, wherein the motherborerepresents the wellbore of the fractured well, and wherein each lateralwellbore represents a respective hydraulic fracture. FIG. 5 illustratesan example equivalent complex well that represents a fractured well.

At step 706, method 700 involves executing, by the computing device andusing the equivalent complex well, a simulation that simulates theperformance of the fractured well. FIG. 6 illustrates an exampleworkflow for implicitly simulating a reservoir that includes a fracturedwell.

In some implementations, generating, by the computing device and basedon the parameters of the fractured well, the equivalent complex wellinvolves modeling each hydraulic fracture by a respective rectangulartube, wherein dimensions of the respective rectangular tube is based ondimensions of the hydraulic fracture.

In some implementations, generating, by the computing device and basedon the parameters of the fractured well, the equivalent complex wellfurther involves generating a motherbore of the equivalent complex wellto represent the wellbore of the fractured well.

In some implementations, generating, by the computing device and basedon the parameters of the fractured well, the equivalent complex wellfurther involves converting the respective rectangular tube into arespective wellbore, where the respective wellbore has an equivalentwellbore diameter calculated based on the dimensions of the respectiverectangular tube, and where a length of the respective wellbore is equalto a height of the respective rectangular tube. FIG. 4A and FIG. 4Billustrate hydraulic fractures modeled as rectangular tubes.

In some implementations, executing, by the computing device and usingthe equivalent complex well, the simulation involves generating, using amulti-segmentation approach, a model of the equivalent complex well,wherein the model includes one or more respective segments for at leastone of the wellbore or the one or more hydraulic fractures.

In some implementations, executing, by the computing device and usingthe equivalent complex well, the simulation further involves generatinga computation matrix for the model of the equivalent complex well,wherein the wellbore computational matrix includes a system of linearalgebraic equations that represent at least one of mass balanceequations, momentum balance equations, or energy balance equations forthe one or more respective segments; and solving the computation matrixand determining that a solution to the computation matrix has convergedto an acceptable tolerance.

The example method 700 shown in FIG. 7 can be modified or reconfiguredto include additional, fewer, or different steps (not shown in FIG. 7 ),which can be performed in the order shown or in a different order.

As an example, after step 706, the method 700 can include generating,based on the simulation, at least one graph that represents individualproduction and performance profiles for the one or more hydraulicfractures; and causing, by the computing device, a display device todisplay the at least one graph. FIGS. 8-12 illustrate simulation resultsof two example simulations.

As another example, the method 700 can include determining, based on thesimulation, a hydraulic fracture design of a well to be drilled; andcontrolling, by the computing device, at least one drilling device todrill the well according to the hydraulic fracture design.

As yet another example, the method 700 can include coupling a solutionof the simulation to a reservoir simulation, wherein the coupling isexplicit, sequential, or implicit.

FIGS. 8-12 illustrate simulation results of two example simulations thatimplement the disclosed methods of simulating fractured wells, accordingto some implementations. The simulations can be executed by a gridsimulator, which can run on one or more computing systems, such as thecomputer system 1300 of FIG. 13 . In these simulations, the testreservoir is a homogenous single phase gas reservoir that includes afractured well. The fractured well includes a horizontal well (forexample, a gas producer) and five hydraulic fractures. The hydraulicfractures are numbered 1 thorough 5, where fracture 1 is the closest tothe heel of the fractured well and fracture 5 is the closest to the toe.The properties of the test reservoir are summarized in Table 1.

TABLE 1 Properties of Test Reservoir Model Size 10 × 10 × 100 AveragePorosity 0.11 Average Permeability 0.1 millidarcy (md) Grid Dimension inX & Y 100 meters (m) Grid Dimension in Z 1 foot

The attributes of the fractured well in the first simulation aresummarized in Table 2. In this simulation, the five hydraulic fractureshave identical geometries.

TABLE 2 Fractured Well Attributes of Simulation 1 Fracture Half Length(X_(f)) 164 ft Fracture Width (W_(f)) 1.36 inch Horizontal WellboreLength 1000 m Fracture Height (h_(f)) 100 ft Fracture spacing intensity200 m

In order for the grid simulator to perform the simulation, the fracturedwell is modeled as a complex well. More specifically, the hydraulicfractures are first modeled as rectangular tubes. The rectangular tubesare then transformed to lateral wellbores. When transforming therectangular tubes to lateral wellbores, the equivalent wellbore diameterfor the laterals is calculated using the attributes from Table 2. Usingthese values, the equivalent wellbore diameter is calculated as:

$d = {{4\frac{2X_{f} \times w_{f}}{2 \times \left( {{2 \times X_{f}} + W_{f}} \right)}} = {{4\frac{328 \times \frac{1.36}{12}}{2 \times \left( {328 + \frac{1.36}{12}} \right)}} = {0.2266{feet}{({ft}).}}}}$Further, the length of the laterals is equal to the fracture height,which is 100 ft. Further, the horizontal wellbore is modeled as amotherbore of a multilateral well that is 1000 m long. Once the complexwell that represents the fractured well is generated, amulti-segmentation approach is used to segment the complex well. In thissimulation, 100 segments are generated for each fracture. A simulationis performed using the segmented complex well model.

FIGS. 8-10 illustrate simulation results of the first simulation. Insome embodiments, the simulation results include respective fractureproduction information for each fracture. FIG. 8 illustrates theindividual fracture performances for the first simulation. Additionally,the simulation results include detailed results for each fracture. Thedetailed results for a fracture include the results corresponding to oneor more segments that represent the fracture. FIG. 9A, FIG. 9B, FIG. 9C,FIG. 9D, and FIG. 9E illustrate the detailed results for fractures 1, 2,3, 4, 5, respectively. Each figure illustrates the production profilefor a fracture over different time periods, where the production profileis the performance of one wing section of the fracture versus measureddepth. The performance can be measured in gas rate in thousand standardcubic feet per day (Mscf/day). As shown in this figures, there is verylittle production away from the motherbore and the highest performanceis in sections closest to the motherbore.

Furthermore, the simulation results at the fracture level includedetails related to the pressure profile of the fractures. FIG. 10illustrates a pressure profile along fracture 1. The x-axis is ameasured depth in feet or meters, and the y-axis is fracture pressure inpsi. The pressure profile shows the wellbore pressure away from themotherbore at the end of the fracture wings and at the intersectionbetween the fractures and the motherbore. The lowest pressure pointexplains why the production for each fracture is showing the highestvalue at the intersection between fracture and the motherbore since thewellbore pressure has the lowest value, which results in the highestdrawdown pressure, and therefore, more gas influx at these segments.

Turning to FIGS. 11-12 , these figures illustrate the simulation resultsof the second simulation. In the second simulation, the properties ofthe five fractures are varied such that each fracture has differentfracture half (X_(f)) length, fracture width (W_(f)), and fractureheight (h_(f)). Table 4 includes a summary of the different geometriesused for the fractures. Note that Equation (1) is used to calculate theequivalent diameters for the fractures.

TABLE 3 Hydraulic Fracture Attributes of Simulation 1 Fracture No. X_(f)(ft) h_(f) (ft) W_(f) (in) d_(eqv) (ft) 1 229.5 100 1.29 0.214949658 2231.92 96 1.36 0.226611297 3 177.11 98 1.48 0.246580811 4 180.72 100 1.50.24991357 5 230.04 94 1.36 0.226610845

FIG. 11 illustrates a comparison for total well gas production rate whenusing uniform fractures (as in the first simulation) with the differentfracture geometry case. This comparison establishes a base line toevaluate how different fracture properties impact production performancefor the gas production well. FIG. 12 illustrates a breakdown of eachfracture performance in the second simulation. More specifically, FIG.12 illustrates how the varied geometries for the fractures played a rolein producing more gas in some fractures (for example, fracture 4) andless gas in other fractures (for example, fractures 1, 2, 3 and 5)compared to the uniform fracture geometry simulation. The solid line forthe case with uniform fracture geometry while the dashed lines forvaried fracture geometry. This detailed look into individual fractureperformance is not possible using existing simulation methods since theydo not accommodate completion level details to be visualizedindividually for each fracture.

FIG. 13 is a block diagram of an example computer system 1300 used toprovide computational functionalities associated with describedalgorithms, methods, functions, processes, flows, and proceduresdescribed in the present disclosure, according to some implementationsof the present disclosure. The illustrated computer 1302 is intended toencompass any computing device such as a server, a desktop computer, alaptop/notebook computer, a wireless data port, a smart phone, apersonal data assistant (PDA), a tablet computing device, or one or moreprocessors within these devices, including physical instances, virtualinstances, or both. The computer 1302 can include input devices such askeypads, keyboards, and touch screens that can accept user information.Also, the computer 1302 can include output devices that can conveyinformation associated with the operation of the computer 1302. Theinformation can include digital data, visual data, audio information, ora combination of information. The information can be presented in agraphical user interface (UI) (or GUI).

The computer 1302 can serve in a role as a client, a network component,a server, a database, a persistency, or components of a computer systemfor performing the subject matter described in the present disclosure.The illustrated computer 1302 is communicably coupled with a network1330. In some implementations, one or more components of the computer1302 can be configured to operate within different environments,including cloud-computing-based environments, local environments, globalenvironments, and combinations of environments.

At a high level, the computer 1302 is an electronic computing deviceoperable to receive, transmit, process, store, and manage data andinformation associated with the described subject matter. According tosome implementations, the computer 1302 can also include, or becommunicably coupled with, an application server, an email server, a webserver, a caching server, a streaming data server, or a combination ofservers.

The computer 1302 can receive requests over network 1330 from a clientapplication (for example, executing on another computer 1302). Thecomputer 1302 can respond to the received requests by processing thereceived requests using software applications. Requests can also be sentto the computer 1302 from internal users (for example, from a commandconsole), external (or third) parties, automated applications, entities,individuals, systems, and computers.

Each of the components of the computer 1302 can communicate using asystem bus 1303. In some implementations, any or all of the componentsof the computer 1302, including hardware or software components, caninterface with each other or the interface 1304 (or a combination ofboth), over the system bus 1303. Interfaces can use an applicationprogramming interface (API) 1312, a service layer 1313, or a combinationof the API 1312 and service layer 1313. The API 1312 can includespecifications for routines, data structures, and object classes. TheAPI 1312 can be either computer-language independent or dependent. TheAPI 1312 can refer to a complete interface, a single function, or a setof APIs.

The service layer 1313 can provide software services to the computer1302 and other components (whether illustrated or not) that arecommunicably coupled to the computer 1302. The functionality of thecomputer 1302 can be accessible for all service consumers using thisservice layer. Software services, such as those provided by the servicelayer 1313, can provide reusable, defined functionalities through adefined interface. For example, the interface can be software written inJAVA, C++, or a language providing data in extensible markup language(XML) format. While illustrated as an integrated component of thecomputer 1302, in alternative implementations, the API 1312 or theservice layer 1313 can be stand-alone components in relation to othercomponents of the computer 1302 and other components communicablycoupled to the computer 1302. Moreover, any or all parts of the API 1312or the service layer 1313 can be implemented as child or sub-modules ofanother software module, enterprise application, or hardware modulewithout departing from the scope of the present disclosure.

The computer 1302 includes an interface 1304. Although illustrated as asingle interface 1304 in FIG. 13 , two or more interfaces 1304 can beused according to particular needs, desires, or particularimplementations of the computer 1302 and the described functionality.The interface 1304 can be used by the computer 1302 for communicatingwith other systems that are connected to the network 1330 (whetherillustrated or not) in a distributed environment. Generally, theinterface 1304 can include, or be implemented using, logic encoded insoftware or hardware (or a combination of software and hardware)operable to communicate with the network 1330. More specifically, theinterface 1304 can include software supporting one or more communicationprotocols associated with communications. As such, the network 1330 orthe interface's hardware can be operable to communicate physical signalswithin and outside of the illustrated computer 1302.

The computer 1302 includes a processor 1305. Although illustrated as asingle processor 1305 in FIG. 13 , two or more processors 1305 can beused according to particular needs, desires, or particularimplementations of the computer 1302 and the described functionality.Generally, the processor 1305 can execute instructions and canmanipulate data to perform the operations of the computer 1302,including operations using algorithms, methods, functions, processes,flows, and procedures as described in the present disclosure.

The computer 1302 also includes a database 1306 that can hold data forthe computer 1302 and other components connected to the network 1330(whether illustrated or not). For example, database 1306 can be anin-memory, conventional, or a database storing data consistent with thepresent disclosure. In some implementations, database 1306 can be acombination of two or more different database types (for example, hybridin-memory and conventional databases) according to particular needs,desires, or particular implementations of the computer 1302 and thedescribed functionality. Although illustrated as a single database 1306in FIG. 13 , two or more databases (of the same, different, orcombination of types) can be used according to particular needs,desires, or particular implementations of the computer 1302 and thedescribed functionality. While database 1306 is illustrated as aninternal component of the computer 1302, in alternative implementations,database 1306 can be external to the computer 1302.

The computer 1302 also includes a memory 13013 that can hold data forthe computer 1302 or a combination of components connected to thenetwork 1330 (whether illustrated or not). Memory 1307 can store anydata consistent with the present disclosure. In some implementations,memory 1307 can be a combination of two or more different types ofmemory (for example, a combination of semiconductor and magneticstorage) according to particular needs, desires, or particularimplementations of the computer 1302 and the described functionality.Although illustrated as a single memory 1307 in FIG. 13 , two or morememories 1307 (of the same, different, or combination of types) can beused according to particular needs, desires, or particularimplementations of the computer 1302 and the described functionality.While memory 1307 is illustrated as an internal component of thecomputer 1302, in alternative implementations, memory 1307 can beexternal to the computer 1302.

The application 1308 can be an algorithmic software engine providingfunctionality according to particular needs, desires, or particularimplementations of the computer 1302 and the described functionality.For example, application 1308 can serve as one or more components,modules, or applications. Further, although illustrated as a singleapplication 1308, the application 1308 can be implemented as multipleapplications 1308 on the computer 1302. In addition, althoughillustrated as internal to the computer 1302, in alternativeimplementations, the application 1308 can be external to the computer1302.

The computer 1302 can also include a power supply 1314. The power supply1314 can include a rechargeable or non-rechargeable battery that can beconfigured to be either user- or non-user-replaceable. In someimplementations, the power supply 1314 can include power-conversion andmanagement circuits, including recharging, standby, and power managementfunctionalities. In some implementations, the power-supply 1314 caninclude a power plug to allow the computer 1302 to be plugged into awall socket or a power source to, for example, power the computer 1302or recharge a rechargeable battery.

There can be any number of computers 1302 associated with, or externalto, a computer system containing computer 1302, with each computer 1302communicating over network 1330. Further, the terms “client,” “user,”and other appropriate terminology can be used interchangeably, asappropriate, without departing from the scope of the present disclosure.Moreover, the present disclosure contemplates that many users can useone computer 1302 and one user can use multiple computers 1302.

Implementations of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Software implementations of the described subjectmatter can be implemented as one or more computer programs. Eachcomputer program can include one or more modules of computer programinstructions encoded on a tangible, non-transitory, computer-readablecomputer-storage medium for execution by, or to control the operationof, data processing apparatus. Alternatively, or additionally, theprogram instructions can be encoded in/on an artificially generatedpropagated signal. For example, the signal can be a machine-generatedelectrical, optical, or electromagnetic signal that is generated toencode information for transmission to a suitable receiver apparatus forexecution by a data processing apparatus. The computer-storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofcomputer-storage mediums.

The terms “data processing apparatus,” “computer,” and “electroniccomputer device” (or equivalent as understood by one of ordinary skillin the art) refer to data processing hardware. For example, a dataprocessing apparatus can encompass all kinds of apparatus, devices, andmachines for processing data, including by way of example, aprogrammable processor, a computer, or multiple processors or computers.The apparatus can also include special purpose logic circuitryincluding, for example, a central processing unit (CPU), a fieldprogrammable gate array (FPGA), or an application specific integratedcircuit (ASIC). In some implementations, the data processing apparatusor special purpose logic circuitry (or a combination of the dataprocessing apparatus or special purpose logic circuitry) can behardware- or software-based (or a combination of both hardware- andsoftware-based). The apparatus can optionally include code that createsan execution environment for computer programs, for example, code thatconstitutes processor firmware, a protocol stack, a database managementsystem, an operating system, or a combination of execution environments.The present disclosure contemplates the use of data processingapparatuses with or without conventional operating systems, for example,LINUX, UNIX, WINDOWS, MAC OS, ANDROID, or IOS.

A computer program, which can also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code, can be written in any form of programming language.Programming languages can include, for example, compiled languages,interpreted languages, declarative languages, or procedural languages.Programs can be deployed in any form, including as standalone programs,modules, components, subroutines, or units for use in a computingenvironment. A computer program can, but need not, correspond to a filein a file system. A program can be stored in a portion of a file thatholds other programs or data, for example, one or more scripts stored ina markup language document, in a single file dedicated to the program inquestion, or in multiple coordinated files storing one or more modules,sub programs, or portions of code. A computer program can be deployedfor execution on one computer or on multiple computers that are located,for example, at one site or distributed across multiple sites that areinterconnected by a communication network. While portions of theprograms illustrated in the various figures may be shown as individualmodules that implement the various features and functionality throughvarious objects, methods, or processes, the programs can instead includea number of sub-modules, third-party services, components, andlibraries. Conversely, the features and functionality of variouscomponents can be combined into single components as appropriate.Thresholds used to make computational determinations can be statically,dynamically, or both statically and dynamically determined.

The methods, processes, or logic flows described in this specificationcan be performed by one or more programmable computers executing one ormore computer programs to perform functions by operating on input dataand generating output. The methods, processes, or logic flows can alsobe performed by, and apparatus can also be implemented as, specialpurpose logic circuitry, for example, a CPU, an FPGA, or an ASIC.

Computers suitable for the execution of a computer program can be basedon one or more of general and special purpose microprocessors and otherkinds of CPUs. The elements of a computer are a CPU for performing orexecuting instructions and one or more memory devices for storinginstructions and data. Generally, a CPU can receive instructions anddata from (and write data to) a memory. A computer can also include, orbe operatively coupled to, one or more mass storage devices for storingdata. In some implementations, a computer can receive data from, andtransfer data to, the mass storage devices including, for example,magnetic, magneto optical disks, or optical disks. Moreover, a computercan be embedded in another device, for example, a mobile telephone, apersonal digital assistant (PDA), a mobile audio or video player, a gameconsole, a global positioning system (GPS) receiver, or a portablestorage device such as a universal serial bus (USB) flash drive.

Computer readable media (transitory or non-transitory, as appropriate)suitable for storing computer program instructions and data can includeall forms of permanent/non-permanent and volatile/nonvolatile memory,media, and memory devices. Computer readable media can include, forexample, semiconductor memory devices such as random access memory(RAM), read only memory (ROM), phase change memory (PRAM), static randomaccess memory (SRAM), dynamic random access memory (DRAM), erasableprogrammable read-only memory (EPROM), electrically erasableprogrammable read-only memory (EEPROM), and flash memory devices.Computer readable media can also include, for example, magnetic devicessuch as tape, cartridges, cassettes, and internal/removable disks.Computer readable media can also include magneto optical disks andoptical memory devices and technologies including, for example, digitalvideo disc (DVD), CD ROM, DVD±R, DVD-RAM, DVD-ROM, HD-DVD, and BLURAY.The memory can store various objects or data, including caches, classes,frameworks, applications, modules, backup data, jobs, web pages, webpage templates, data structures, database tables, repositories, anddynamic information. Types of objects and data stored in memory caninclude parameters, variables, algorithms, instructions, rules,constraints, and references. Additionally, the memory can include logs,policies, security or access data, and reporting files. The processorand the memory can be supplemented by, or incorporated in, specialpurpose logic circuitry.

Implementations of the subject matter described in the presentdisclosure can be implemented on a computer having a display device forproviding interaction with a user, including displaying information to(and receiving input from) the user. Types of display devices caninclude, for example, a cathode ray tube (CRT), a liquid crystal display(LCD), a light-emitting diode (LED), and a plasma monitor. Displaydevices can include a keyboard and pointing devices including, forexample, a mouse, a trackball, or a trackpad. User input can also beprovided to the computer through the use of a touchscreen, such as atablet computer surface with pressure sensitivity or a multi-touchscreen using capacitive or electric sensing. Other kinds of devices canbe used to provide for interaction with a user, including to receiveuser feedback including, for example, sensory feedback including visualfeedback, auditory feedback, or tactile feedback. Input from the usercan be received in the form of acoustic, speech, or tactile input. Inaddition, a computer can interact with a user by sending documents to,and receiving documents from, a device that is used by the user. Forexample, the computer can send web pages to a web browser on a user'sclient device in response to requests received from the web browser.

The term “graphical user interface,” or “GUI,” can be used in thesingular or the plural to describe one or more graphical user interfacesand each of the displays of a particular graphical user interface.Therefore, a GUI can represent any graphical user interface, including,but not limited to, a web browser, a touch screen, or a command lineinterface (CLI) that processes information and efficiently presents theinformation results to the user. In general, a GUI can include aplurality of user interface (UI) elements, some or all associated with aweb browser, such as interactive fields, pull-down lists, and buttons.These and other UI elements can be related to or represent the functionsof the web browser.

Implementations of the subject matter described in this specificationcan be implemented in a computing system that includes a back endcomponent, for example, as a data server, or that includes a middlewarecomponent, for example, an application server. Moreover, the computingsystem can include a front-end component, for example, a client computerhaving one or both of a graphical user interface or a Web browserthrough which a user can interact with the computer. The components ofthe system can be interconnected by any form or medium of wireline orwireless digital data communication (or a combination of datacommunication) in a communication network. Examples of communicationnetworks include a local area network (LAN), a radio access network(RAN), a metropolitan area network (MAN), a wide area network (WAN),Worldwide Interoperability for Microwave Access (WIMAX), a wirelesslocal area network (WLAN) (for example, using 802.11 a/b/g/n or 802.20or a combination of protocols), all or a portion of the Internet, or anyother communication system or systems at one or more locations (or acombination of communication networks). The network can communicatewith, for example, Internet Protocol (IP) packets, frame relay frames,asynchronous transfer mode (ATM) cells, voice, video, data, or acombination of communication types between network addresses.

The computing system can include clients and servers. A client andserver can generally be remote from each other and can typicallyinteract through a communication network. The relationship of client andserver can arise by virtue of computer programs running on therespective computers and having a client-server relationship.

Cluster file systems can be any file system type accessible frommultiple servers for read and update. Locking or consistency trackingmay not be necessary since the locking of exchange file system can bedone at application layer. Furthermore, Unicode data files can bedifferent from non-Unicode data files.

FIG. 14 is a partial schematic perspective view of an example rig system100 for drilling and producing a well. The well can extend from thesurface through the Earth to one or more subterranean zones of interest.The example rig system 1400 includes a drill floor 1402 positioned abovethe surface, a wellhead 1404, a drill string assembly 1406 supported bythe rig structure, and a fluid circulation system 1408 to filter useddrilling fluid from the wellbore and provide clean drilling fluid to thedrill string assembly 1406. For example, the example rig system 1400 ofFIG. 14 is shown as a drill rig capable of performing a drillingoperation with the rig system 1400 supporting the drill string assembly1406 over a wellbore. The wellhead 1404 can be used to support casing orother well components or equipment into the wellbore of the well.

The derrick or mast is a support framework mounted on the drill floor1402 and positioned over the wellbore to support the components of thedrill string assembly 1406 during drilling operations. A crown block1412 forms a longitudinally-fixed top of the derrick, and connects to atravelling block 1414 with a drilling line including a set of wire ropesor cables. The crown block 1412 and the travelling block 1414 supportthe drill string assembly 1406 via a swivel 1416, a kelly 1418, or a topdrive system (not shown). Longitudinal movement of the travelling block1414 relative to the crown block 1412 of the drill string assembly 1406acts to move the drill string assembly 1406 longitudinally upward anddownward. The swivel 1416, connected to and hung by the travelling block1414 and a rotary hook, allows free rotation of the drill stringassembly 1406 and provides a connection to a kelly hose 1420, which is ahose that flows drilling fluid from a drilling fluid supply of thecirculation system 1408 to the drill string assembly 1406. A standpipe1422 mounted on the drill floor 1402 guides at least a portion of thekelly hose 1420 to a location proximate to the drill string assembly1406. The kelly 1418 is a hexagonal device suspended from the swivel1416 and connected to a longitudinal top of the drill string assembly1406, and the kelly 1418 turns with the drill string assembly 1406 asthe rotary table 1442 of the drill string assembly turns.

In the example rig system 1400 of FIG. 14 , the drill string assembly1406 is made up of drill pipes with a drill bit (not shown) at alongitudinally bottom end of the drill string. The drill pipe caninclude hollow steel piping, and the drill bit can include cuttingtools, such as blades, discs, rollers, cutters, or a combination ofthese, to cut into the formation and form the wellbore. The drill bitrotates and penetrates through rock formations below the surface underthe combined effect of axial load and rotation of the drill stringassembly 1406. In some implementations, the kelly 1418 and swivel 1416can be replaced by a top drive that allows the drill string assembly1406 to spin and drill. The wellhead assembly 1404 can also include adrawworks 1424 and a deadline anchor 1426, where the drawworks 1424includes a winch that acts as a hoisting system to reel the drillingline in and out to raise and lower the drill string assembly 1406 by afast line 1425. The deadline anchor 1426 fixes the drilling lineopposite the drawworks 1424 by a deadline 1427, and can measure thesuspended load (or hook load) on the rotary hook. The weight on bit(WOB) can be measured when the drill bit is at the bottom the wellbore.The wellhead assembly 1404 also includes a blowout preventer 1450positioned at the surface of the well and below (but often connected to)the drill floor 1402. The blowout preventer 1450 acts to prevent wellblowouts caused by formation fluid entering the wellbore, displacingdrilling fluid, and flowing to the surface at a pressure greater thanatmospheric pressure. The blowout preventer 1450 can close around (andin some instances, through) the drill string assembly 1406 and seal offthe space between the drill string and the wellbore wall. The blowoutpreventer 1450 is described in more detail later.

During a drilling operation of the well, the circulation system 1408circulates drilling fluid from the wellbore to the drill string assembly1406, filters used drilling fluid from the wellbore, and provides cleandrilling fluid to the drill string assembly 1406. The examplecirculation system 1408 includes a fluid pump 1430 that fluidly connectsto and provides drilling fluid to drill string assembly 1406 via thekelly hose 1420 and the standpipe 1422. The circulation system 1408 alsoincludes a flow-out line 1432, a shale shaker 1434, a settling pit 1436,and a suction pit 1438. In a drilling operation, the circulation system1408 pumps drilling fluid from the surface, through the drill stringassembly 1406, out the drill bit and back up the annulus of thewellbore, where the annulus is the space between the drill pipe and theformation or casing. The density of the drilling fluid is intended to begreater than the formation pressures to prevent formation fluids fromentering the annulus and flowing to the surface and less than themechanical strength of the formation, as a greater density may fracturethe formation, thereby creating a path for the drilling fluids to gointo the formation. Apart from well control, drilling fluids can alsocool the drill bit and lift rock cuttings from the drilled formation upthe annulus and to the surface to be filtered out and treated before itis pumped down the drill string assembly 1406 again. The drilling fluidreturns in the annulus with rock cuttings and flows out to the flow-outline 1432, which connects to and provides the fluid to the shale shaker1434. The flow line is an inclined pipe that directs the drilling fluidfrom the annulus to the shale shaker 1434. The shale shaker 1434includes a mesh-like surface to separate the coarse rock cuttings fromthe drilling fluid, and finer rock cuttings and drilling fluid then gothrough the settling pit 1436 to the suction pit 1436. The circulationsystem 1408 includes a mud hopper 1440 into which materials (forexample, to provide dispersion, rapid hydration, and uniform mixing) canbe introduced to the circulation system 1408. The fluid pump 1430 cyclesthe drilling fluid up the standpipe 1422 through the swivel 1416 andback into the drill string assembly 1406 to go back into the well.

The example wellhead assembly 1404 can take a variety of forms andinclude a number of different components. For example, the wellheadassembly 1404 can include additional or different components than theexample shown in FIG. 14 . Similarly, the circulation system 1408 caninclude additional or different components than the example shown inFIG. 14 .

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of what may beclaimed, but rather as descriptions of features that may be specific toparticular implementations. Certain features that are described in thisspecification in the context of separate implementations can also beimplemented, in combination, in a single implementation. Conversely,various features that are described in the context of a singleimplementation can also be implemented in multiple implementations,separately, or in any suitable sub-combination. Moreover, althoughpreviously described features may be described as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can, in some cases, be excised from thecombination, and the claimed combination may be directed to asub-combination or variation of a sub-combination.

Particular implementations of the subject matter have been described.Other implementations, alterations, and permutations of the describedimplementations are within the scope of the following claims as will beapparent to those skilled in the art. While operations are depicted inthe drawings or claims in a particular order, this should not beunderstood as requiring that such operations be performed in theparticular order shown or in sequential order, or that all illustratedoperations be performed (some operations may be considered optional), toachieve desirable results. In certain circumstances, multitasking orparallel processing (or a combination of multitasking and parallelprocessing) may be advantageous and performed as deemed appropriate.

Moreover, the separation or integration of various system modules andcomponents in the previously described implementations should not beunderstood as requiring such separation or integration in allimplementations, and it should be understood that the described programcomponents and systems can generally be integrated together in a singlesoftware product or packaged into multiple software products.

Accordingly, the previously described example implementations do notdefine or constrain the present disclosure. Other changes,substitutions, and alterations are also possible without departing fromthe spirit and scope of the present disclosure.

Furthermore, any claimed implementation is considered to be applicableto at least a computer-implemented method; a non-transitory,computer-readable medium storing computer-readable instructions toperform the computer-implemented method; and a computer systemcomprising a computer memory interoperably coupled with a hardwareprocessor configured to perform the computer-implemented method or theinstructions stored on the non-transitory, computer-readable medium.

A number of embodiments of the present disclosure have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the presentdisclosure. Accordingly, other embodiments are within the scope of thefollowing claims.

Various modifications, alterations, and permutations of the disclosedimplementations can be made and will be readily apparent to those ofordinary skill in the art, and the general principles defined may beapplied to other implementations and applications, without departingfrom scope of the disclosure. In some instances, details unnecessary toobtain an understanding of the described subject matter may be omittedso as to not obscure one or more described implementations withunnecessary detail and inasmuch as such details are within the skill ofone of ordinary skill in the art. The present disclosure is not intendedto be limited to the described or illustrated implementations, but to beaccorded the widest scope consistent with the described principles andfeatures.

What is claimed is:
 1. A computer-implemented method for simulatingperformance of a fractured well, the method comprising: receiving, by acomputing device, parameters of the fractured well, wherein thefractured well comprises a wellbore and one or more hydraulic fracturesextending from the wellbore; generating, by the computing device andbased on the parameters of the fractured well, an equivalent complexwell that represents the fractured well; executing, by the computingdevice and using the equivalent complex well, a simulation thatsimulates the performance of the fractured well; determining, based on asimulated performance of the fractured well, a hydraulic fracture designof a well to be drilled, wherein the hydraulic fracture design specifiesa hydraulic fracture spacing intensity; and controlling, by thecomputing device and based on the hydraulic fracture design, at leastone drilling device to drill the well according to the hydraulicfracture design such that adjacent fractures in the drilled wellmaintain a distance that is no less than the hydraulic fracture spacingintensity, wherein generating, by the computing device and based on theparameters of the fractured well, the equivalent complex well comprises:modeling each hydraulic fracture by a respective rectangular tube,wherein dimensions of the respective rectangular tube is based ondimensions of the hydraulic fracture.
 2. The computer-implemented methodof claim 1, wherein the equivalent complex well is a multilateral wellthat includes a motherbore and one or more lateral wellbores, whereinthe motherbore represents the wellbore of the fractured well, andwherein each lateral wellbore represents a respective hydraulicfracture.
 3. The computer-implemented method of claim 1, wherein theparameters of the fractured well comprise at least one of: (i) a lengthof the wellbore, (ii) respective fracture half-lengths (X_(f)) of theone or more hydraulic fractures, (iii) respective fracture heights(h_(f)) of the one or more hydraulic fractures, (iv) respective fracturewidths (W_(f)) of the one or more hydraulic fractures, or (v) thehydraulic fracture spacing intensity.
 4. The computer-implemented methodof claim 1, wherein generating, by the computing device and based on theparameters of the fractured well, the equivalent complex well furthercomprises: generating a motherbore of the equivalent complex well torepresent the wellbore of the fractured well.
 5. Thecomputer-implemented method of claim 1, wherein generating, by thecomputing device and based on the parameters of the fractured well, theequivalent complex well further comprises: converting the respectiverectangular tube into a respective wellbore, wherein the respectivewellbore has an equivalent wellbore diameter calculated based on thedimensions of the respective rectangular tube, and wherein a length ofthe respective wellbore is equal to a height of the respectiverectangular tube.
 6. The computer-implemented method of claim 1, whereinexecuting, by the computing device and using the equivalent complexwell, the simulation comprises: generating, using a multi-segmentationapproach, a model of the equivalent complex well, wherein the modelcomprises one or more respective segments for at least one of thewellbore or the one or more hydraulic fractures.
 7. Thecomputer-implemented method of claim 6, wherein executing, by thecomputing device and using the equivalent complex well, the simulationfurther comprises: generating a computation matrix for the model of theequivalent complex well, wherein the wellbore computational matrixcomprises a system of linear algebraic equations that represent at leastone of mass balance equations, momentum balance equations, or energybalance equations for the one or more respective segments; and solvingthe computation matrix and determining that a solution to thecomputation matrix has converged to an acceptable tolerance.
 8. Thecomputer-implemented method of claim 1, further comprising: generating,based on the simulation, at least one graph that represents individualproduction and performance profiles for the one or more hydraulicfractures; and causing, by the computing device, a display device todisplay the at least one graph.
 9. The computer-implemented method ofclaim 1, further comprising: coupling a solution of the simulation to areservoir simulation, wherein the coupling is explicit, sequential, orimplicit.
 10. A non-transitory computer-readable medium storing one ormore instructions executable by a computer system to perform operationsfor simulating performance of a fractured well, the operationscomprising: receiving, by a computing device, parameters of thefractured well, wherein the fractured well comprises a wellbore and oneor more hydraulic fractures extending from the wellbore; generating, bythe computing device and based on the parameters of the fractured well,an equivalent complex well that represents the fractured well;executing, by the computing device and using the equivalent complexwell, a simulation that simulates the performance of the fractured well;determining, based on a simulated performance of the fractured well, ahydraulic fracture design of a well to be drilled, wherein the hydraulicfracture design specifies a hydraulic fracture spacing intensity; andcontrolling, by the computing device and based on the hydraulic fracturedesign, at least one drilling device to drill the well according to thehydraulic fracture design such that adjacent fractures in the drilledwell maintain a distance that is no less than the hydraulic fracturespacing intensity, wherein generating, by the computing device and basedon the parameters of the fractured well, the equivalent complex wellcomprises: modeling each hydraulic fracture by a respective rectangulartube, wherein dimensions of the respective rectangular tube is based ondimensions of the hydraulic fracture.
 11. The non-transitorycomputer-readable medium of claim 10, wherein the equivalent complexwell is a multilateral well that includes a motherbore and one or morelateral wellbores, wherein the motherbore represents the wellbore of thefractured well, and wherein each lateral wellbore represents arespective hydraulic fracture.
 12. The non-transitory computer-readablemedium of claim 10, wherein the parameters of the fractured wellcomprise at least one of: (i) a length of the wellbore, (ii) respectivefracture half-lengths (X_(f)) of the one or more hydraulic fractures,(iii) respective fracture heights (h_(f)) of the one or more hydraulicfractures, (iv) respective fracture widths (W_(f)) of the one or morehydraulic fractures, or (v) hydraulic fracture spacing intensity. 13.The non-transitory computer-readable medium of claim 10, whereingenerating, by the computing device and based on the parameters of thefractured well, the equivalent complex well further comprises:generating a motherbore of the equivalent complex well to represent thewellbore of the fractured well.
 14. The non-transitory computer-readablemedium of claim 10, wherein generating, by the computing device andbased on the parameters of the fractured well, the equivalent complexwell further comprises: converting the respective rectangular tube intoa respective wellbore, wherein the respective wellbore has an equivalentwellbore diameter calculated based on the dimensions of the respectiverectangular tube, and wherein a length of the respective wellbore isequal to a height of the respective rectangular tube.
 15. A system forsimulating performance of a fractured well, the system comprising: oneor more processors; and a non-transitory computer-readable storagemedium coupled to the one or more processors and storing programminginstructions for execution by the one or more processors, theprogramming instructions instructing the one or more processors toperform operations comprising: receiving, by a computing device,parameters of the fractured well, wherein the fractured well comprises awellbore and one or more hydraulic fractures extending from thewellbore; generating, by the computing device and based on theparameters of the fractured well, an equivalent complex well thatrepresents the fractured well; executing, by the computing device andusing the equivalent complex well, a simulation that simulates theperformance of the fractured well; determining, based on a simulatedperformance of the fractured well, a hydraulic fracture design of a wellto be drilled, wherein the hydraulic fracture design specifies ahydraulic fracture spacing intensity; and controlling, by the computingdevice and based on the hydraulic fracture design, at least one drillingdevice to drill the well according to the hydraulic fracture design suchthat adjacent fractures in the drilled well maintain a distance that isno less than the hydraulic fracture spacing intensity, whereingenerating, by the computing device and based on the parameters of thefractured well, the equivalent complex well comprises: modeling eachhydraulic fracture by a respective rectangular tube, wherein dimensionsof the respective rectangular tube is based on dimensions of thehydraulic fracture.
 16. The system of claim 15, wherein the equivalentcomplex well is a multilateral well that includes a motherbore and oneor more lateral wellbores, wherein the motherbore represents thewellbore of the fractured well, and wherein each lateral wellborerepresents a respective hydraulic fracture.
 17. The system of claim 15,wherein the parameters of the fractured well comprise at least one of:(i) a length of the wellbore, (ii) respective fracture half-lengths(X_(f)) of the one or more hydraulic fractures, (iii) respectivefracture heights (h_(f)) of the one or more hydraulic fractures, (iv)respective fracture widths (W_(f)) of the one or more hydraulicfractures, or (v) the hydraulic fracture spacing intensity.